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</pre>
==1. Introduction==
===1.1. Outline of the Project : Inquiry Into Inquiry===
====1.1.1. Problem====
1.1.1. Problem
<pre>
This research is oriented toward a single problem:
This research is oriented toward a single problem:
the general trend of all forms of reasoning that lead to the features
the general trend of all forms of reasoning that lead to the features
of scientific investigation as their ultimate development.
of scientific investigation as their ultimate development.
</pre>
====1.1.2. Method====
1.1.2. Method
<pre>
How will I approach this problem about the nature of inquiry?
How will I approach this problem about the nature of inquiry?
Taking these initial stages into consideration, I can describe the main
Taking these initial stages into consideration, I can describe the main
modalities of this research in greater detail.
modalities of this research in greater detail.
</pre>
=====1.1.2.1. The Paradigmatic and Process-Analytic Phase=====
1.1.2.1. The Paradigmatic and Process-Analytic Phase
<pre>
In this phase I describe the performance and the competence
In this phase I describe the performance and the competence
of intelligent agents in terms of a variety of formal systems:
of intelligent agents in terms of a variety of formal systems:
that is to say, a testable (defeasible or falsifiable) construal of how a process
that is to say, a testable (defeasible or falsifiable) construal of how a process
is actually, might be possibly, or ought to be optimally carried out.
is actually, might be possibly, or ought to be optimally carried out.
</pre>
=====1.1.2.2. The Paraphrastic and Faculty-Synthetic Phase=====
1.1.2.2. The Paraphrastic and Faculty-Synthetic Phase
<pre>
The closely allied techniques of task analysis and software development that are
The closely allied techniques of task analysis and software development that are
known as "step-wise refinement" and "top-down programming" in computer science
known as "step-wise refinement" and "top-down programming" in computer science
the design of computer programs that can fulfill them, at least,
the design of computer programs that can fulfill them, at least,
to whatever extent makes sense with regard to the ends in view.
to whatever extent makes sense with regard to the ends in view.
</pre>
=====1.1.2.3. Reprise of Methods=====
1.1.2.3. Reprise of Methods
<pre>
The whole array of methods will be typical of the "top-down" strategies
The whole array of methods will be typical of the "top-down" strategies
used in artificial intelligence research, involving the conceptual and
used in artificial intelligence research, involving the conceptual and
the runners, shoots, and tendrils of research tend to interleave
the runners, shoots, and tendrils of research tend to interleave
and intertwine as they will.
and intertwine as they will.
</pre>
====1.1.3. Criterion====
1.1.3. Criterion
<pre>
When is enough enough? What measure can I use to tell if my effort is working?
When is enough enough? What measure can I use to tell if my effort is working?
What information is critical in deciding whether my exercise of the method is
What information is critical in deciding whether my exercise of the method is
less hesitation, more determination is manifested by
less hesitation, more determination is manifested by
less vacillation.
less vacillation.
</pre>
====1.1.4. Application====
1.1.4. Application
<pre>
Where can the results be used?
Where can the results be used?
logic (the normative study of how we ought to think in order to accomplish
logic (the normative study of how we ought to think in order to accomplish
the goals of reasoning).
the goals of reasoning).
</pre>
===1.2. Onus of the Project: No Way But Inquiry===
1.2. Onus of the Project: No Way But Inquiry
<pre>
At the beginning of inquiry there is nothing for me to work with
At the beginning of inquiry there is nothing for me to work with
but the actual constellation of doubts and beliefs that I have at
but the actual constellation of doubts and beliefs that I have at
patterns of strategy are routinely more successful in the long run
patterns of strategy are routinely more successful in the long run
than others.
than others.
</pre>
====1.2.1. A Modulating Prelude====
1.2.1. A Modulating Prelude
<pre>
If I aim to devise the kind of computational support that can give the
If I aim to devise the kind of computational support that can give the
greatest assistance to inquiry, then it must be able to come in at the
greatest assistance to inquiry, then it must be able to come in at the
in their specific contents and peculiar to the states of the
in their specific contents and peculiar to the states of the
particular agents to which they attach.
particular agents to which they attach.
</pre>
====1.2.2. A Fugitive Canon====
<pre>
The principal difficulties associated with
this task appear to spring from two roots.
The principal difficulties associated with
this task appear to spring from two roots.
First, there is the issue of "computational mediation". In using the sorts
First, there is the issue of "computational mediation". In using the sorts
experiences of oneself and others, but in points of form to compare
experiences of oneself and others, but in points of form to compare
them with the structures present in mathematical models?
them with the structures present in mathematical models?
</pre>
===1.3. Option of the Project : A Way Up To Inquiry===
1.3. Option of the Project: A Way Up To Inquiry
<pre>
I begin with an informal examination of the concept of inquiry.
I begin with an informal examination of the concept of inquiry.
serve as proxies for unknown components and indicate tentative
serve as proxies for unknown components and indicate tentative
analyses of faculties in question.
analyses of faculties in question.
</pre>
====1.3.1. Initial Analysis of Inquiry -- Allegro Aperto====
1.3.1. Initial Analysis of Inquiry -- Allegro Aperto
<pre>
If the faculty of inquiry is a coherent power, then it has
If the faculty of inquiry is a coherent power, then it has
an active or instrumental face, a passive or objective face,
an active or instrumental face, a passive or objective face,
In accord with this plan, the main body of this Division (1.3) is devoted
In accord with this plan, the main body of this Division (1.3) is devoted
to a discussion of formalization. y_0 = y y >= {d, f}{d, f} >= {f}{d}.
to a discussion of formalization. y_0 = y y >= {d, f}{d, f} >= {f}{d}.
</pre>
====1.3.2. Discussion of Discussion====
1.3.2. Discussion of Discussion
<pre>
But first, I nearly skipped a step. Though it might present itself as
But first, I nearly skipped a step. Though it might present itself as
an interruption, a topic so easy that I almost omitted it altogether
an interruption, a topic so easy that I almost omitted it altogether
digressionary narrative into a properly directed inquiry. This brings
digressionary narrative into a properly directed inquiry. This brings
an end to my initial discussion of "discussion".
an end to my initial discussion of "discussion".
</pre>
====1.3.3. Discussion of Formalization : General Topics====
1.3.3. Discussion of Formalization: General Topics
<pre>
Because this project makes constant use of formal models
Because this project makes constant use of formal models
of phenomenal processes, it is incumbent on me at this
of phenomenal processes, it is incumbent on me at this
that I will use throughout this work and to preview
that I will use throughout this work and to preview
a concrete example of its application.
a concrete example of its application.
</pre>
1.3.3.1. A Formal Charge
=====1.3.3.1. A Formal Charge=====
<pre>
An introduction to the topic of formalization, if proper,
An introduction to the topic of formalization, if proper,
is obliged to begin informally. But it will be my constant
is obliged to begin informally. But it will be my constant
out the form, if not the substance, of what it
out the form, if not the substance, of what it
does, or an aspect thereof.
does, or an aspect thereof.
</pre>
=====1.3.3.2. A Formalization of Formalization?=====
1.3.3.2. A Formalization of Formalization?
<pre>
An immediate application of the above rules is presented here, in hopes of
An immediate application of the above rules is presented here, in hopes of
giving the reader a concrete illustration of their use in a ready example,
giving the reader a concrete illustration of their use in a ready example,
in its present state of completion would be far too tedious and tenuous
in its present state of completion would be far too tedious and tenuous
to escape expurgation.
to escape expurgation.
</pre>
=====1.3.3.3. A Formalization of Discussion?=====
1.3.3.3. A Formalization of Discussion?
<pre>
The previous Subsection took the concept of "formalization" as an example
The previous Subsection took the concept of "formalization" as an example
of a topic that a writer might try to translate from informal discussion
of a topic that a writer might try to translate from informal discussion
Just what is involved in achieving the object of a motivated discussion?
Just what is involved in achieving the object of a motivated discussion?
Can these intentions be formalized? y_0 = y y >= {d, f}{d, f} >= {d}{f}.
Can these intentions be formalized? y_0 = y y >= {d, f}{d, f} >= {d}{f}.
The writer's task is not to create meaning from nothing,
The writer's task is not to create meaning from nothing,
the reader's part that is extensible in non-trivial ways.
the reader's part that is extensible in non-trivial ways.
At this point, the discussion has touched on a topic, in one of its
At this point, the discussion has touched on a topic, in one of its
manifold aspects, that it will encounter repeatedly, under a variety
manifold aspects, that it will encounter repeatedly, under a variety
of aspects, throughout this work. In recognition of this circumstance,
of aspects, throughout this work. In recognition of this circumstance,
together into the qualifications of inquiry and a definition
together into the qualifications of inquiry and a definition
of what exactly is desired in order to constitute knowledge?
of what exactly is desired in order to constitute knowledge?
</pre>
=====1.3.3.4. A Concept of Formalization=====
1.3.3.4. A Concept of Formalization
<pre>
The concept of formalization is intended to cover the whole collection
The concept of formalization is intended to cover the whole collection
of activities that serve to build a relation between casual discussions,
of activities that serve to build a relation between casual discussions,
the object language, the domain of structures and processes that can be
the object language, the domain of structures and processes that can be
studied as a completely formalized object.
studied as a completely formalized object.
</pre>
=====1.3.3.5. A Formal Approach=====
1.3.3.5. A Formal Approach
<pre>
I plan to approach the issue of formalization from a slightly different angle,
I plan to approach the issue of formalization from a slightly different angle,
proceeding through an analysis of the medium of interpretation and developing
proceeding through an analysis of the medium of interpretation and developing
that serves to convey an appearance of knowledge in a place where very
that serves to convey an appearance of knowledge in a place where very
little is known about the subject itself.
little is known about the subject itself.
A meta-language corresponds to what I call an "interpretive framework".
A meta-language corresponds to what I call an "interpretive framework".
they may have little surplus memory capacity to memorandize the big picture,
they may have little surplus memory capacity to memorandize the big picture,
even when these acts of reflection and critique are permitted in principle.
even when these acts of reflection and critique are permitted in principle.
An object language is a special case of the kind of formal system that is
An object language is a special case of the kind of formal system that is
permeabilities and a permanent hierarchy of effabilities
permeabilities and a permanent hierarchy of effabilities
in language.
in language.
The grounds of discussion that I'm raking over here constellate a rather
The grounds of discussion that I'm raking over here constellate a rather
must be possible to describe it within the frame
must be possible to describe it within the frame
of this informally discursive universe.
of this informally discursive universe.
</pre>
=====1.3.3.6. A Formal Development=====
1.3.3.6. A Formal Development
<pre>
The point of view I take on the origin and development of formal models
The point of view I take on the origin and development of formal models
is that they arise with agents retracing structures that already exist
is that they arise with agents retracing structures that already exist
or an analytically representative recipe, or (3) whether it instead insistently
or an analytically representative recipe, or (3) whether it instead insistently
obscures what portion of its domain it manages to cover.
obscures what portion of its domain it manages to cover.
</pre>
=====1.3.3.7. A Formal Persuasion=====
1.3.3.7. A Formal Persuasion
<pre>
An interpretive system can be taken up with very little fanfare, since it
An interpretive system can be taken up with very little fanfare, since it
does not enjoin one to declare undying allegiance to a particular point of
does not enjoin one to declare undying allegiance to a particular point of
of the fact that this is not likely
of the fact that this is not likely
to be a universally shared opinion.
to be a universally shared opinion.
</pre>
====1.3.4. Discussion of Formalization : Concrete Examples====
1.3.4. Discussion of Formalization: Concrete Examples
<pre>
Section 1.3.3 outlined a variety of general issues surrounding the concept
Section 1.3.3 outlined a variety of general issues surrounding the concept
of formalization. Section 1.3.5 will plot the specific objectives of this
of formalization. Section 1.3.5 will plot the specific objectives of this
that are intended to illustrate the kinds of mathematical objects
that are intended to illustrate the kinds of mathematical objects
I have in mind using as formal models.
I have in mind using as formal models.
</pre>
=====1.3.4.1. Formal Models : A Sketch=====
1.3.4.1. Formal Models: A Sketch
<pre>
To sketch as briefly as possible the features of the modeling activity
To sketch as briefly as possible the features of the modeling activity
that are most relevant to our present purpose: The modeler begins with
that are most relevant to our present purpose: The modeler begins with
the effort to try lifting one or another edge of these frameworks
the effort to try lifting one or another edge of these frameworks
and backdrops into the light, at least for a time.
and backdrops into the light, at least for a time.
</pre>
=====1.3.4.2. Sign Relations : A Primer=====
1.3.4.2. Sign Relations: A Primer
<pre>
To the extent that their structures and functions can be discussed at all,
To the extent that their structures and functions can be discussed at all,
it appears likely at this point that all of the formal entities destined
it appears likely at this point that all of the formal entities destined
of signs is specialized to treat from structural and comparative points
of signs is specialized to treat from structural and comparative points
of view.
of view.
Because the examples in this Section (1.3.4) have been artificially
Because the examples in this Section (1.3.4) have been artificially
occasionally used in the philosophy of language to point out the needed
occasionally used in the philosophy of language to point out the needed
distinctions.
distinctions.
One aspect of the meaning of a sign is concerned with the reference
One aspect of the meaning of a sign is concerned with the reference
use have properties that quickly bring the usual prospects of
use have properties that quickly bring the usual prospects of
formal semantics to a screeching halt.
formal semantics to a screeching halt.
The other dyadic aspects of meaning that might be considered concern
The other dyadic aspects of meaning that might be considered concern
of this material does not interfere with understanding the purely
of this material does not interfere with understanding the purely
formal aspects of the present Example.
formal aspects of the present Example.
Formally speaking, the connotative and intentional
Formally speaking, the connotative and intentional
of sign relations that form the necessary conditions for achieving these
of sign relations that form the necessary conditions for achieving these
aims and thus for being able to conduct coherently directed inquiries.
aims and thus for being able to conduct coherently directed inquiries.
</pre>
=====1.3.4.3. Semiotic Equivalence Relations=====
1.3.4.3. Semiotic Equivalence Relations
If one examines the sign relations L(A) and L(B) that are associated with
If one examines the sign relations L(A) and L(B) that are associated with
| "u" | "B" |
| "u" | "B" |
o---------------o---------------o
o---------------o---------------o
In order to discuss this type of situation further,
In order to discuss this type of situation further,
{{"A", "u"}, {"B", "i"}}.
{{"A", "u"}, {"B", "i"}}.
</pre>
=====1.3.4.4. Graphical Representations=====
1.3.4.4. Graphical Representations
<pre>
The dyadic components of sign relations can be given graph-theoretic
The dyadic components of sign relations can be given graph-theoretic
representations as "directed graphs", or "digraphs" for short, that
representations as "directed graphs", or "digraphs" for short, that
are involved when the interpreters A and B evaluate the signs in S
are involved when the interpreters A and B evaluate the signs in S
according to their own frames of reference.
according to their own frames of reference.
The connotative components Con L(A) and Con L(B) can be represented
The connotative components Con L(A) and Con L(B) can be represented
different sorts of relational structures on the same set of points,
different sorts of relational structures on the same set of points,
heralds a topic that will be developed extensively in the sequel.
heralds a topic that will be developed extensively in the sequel.
</pre>
=====1.3.4.5. Taking Stock=====
1.3.4.5. Taking Stock
<pre>
So far, my discussion of the discussion between A and B, in the picture that
So far, my discussion of the discussion between A and B, in the picture that
it gives of sign relations and their connection to the imagined processes of
it gives of sign relations and their connection to the imagined processes of
clues to significant deficits in theory and technique, and that can serve
clues to significant deficits in theory and technique, and that can serve
to point out directions for future improvements.
to point out directions for future improvements.
</pre>
=====1.3.4.6. The "Meta" Question=====
1.3.4.6. The "Meta" Question
<pre>
There is one point of common contention that I finessed from play
There is one point of common contention that I finessed from play
in my handling of the transaction between A and B, even though it
in my handling of the transaction between A and B, even though it
conventional symbols for their objects but fully iconic
conventional symbols for their objects but fully iconic
representations of their objective operative structure.
representations of their objective operative structure.
</pre>
=====1.3.4.7. Iconic Signs=====
1.3.4.7. Iconic Signs
<pre>
In the pragmatic theory of signs, an "icon" is a sign that accomplishes
In the pragmatic theory of signs, an "icon" is a sign that accomplishes
its representation, including the projects of denotation and connotation,
its representation, including the projects of denotation and connotation,
sign relations would have several portions that look identical to pieces of
sign relations would have several portions that look identical to pieces of
the very sign relational Tables that are being placed under formal review.
the very sign relational Tables that are being placed under formal review.
</pre>
=====1.3.4.8. The Conflict of Interpretations=====
1.3.4.8. The Conflict of Interpretations
<pre>
One discrepancy that needs to be documented at this point
One discrepancy that needs to be documented at this point
can be observed in the conflict of interpretations between
can be observed in the conflict of interpretations between
that keeps indexical signs persistently attached to their interpreters
that keeps indexical signs persistently attached to their interpreters
of reference.
of reference.
</pre>
=====1.3.4.9. Indexical Signs=====
1.3.4.9. Indexical Signs
<pre>
In the pragmatic theory of signs, an "index" is a sign that achieves its
In the pragmatic theory of signs, an "index" is a sign that achieves its
representation of an object by virtue of an actual connection with it.
representation of an object by virtue of an actual connection with it.
necessity "essential connections" to whatever
necessity "essential connections" to whatever
objects they do in fact denote.
objects they do in fact denote.
Saying that an index is a property of an instance of an object almost
Saying that an index is a property of an instance of an object almost
the experience, in this way connecting the diverse abstractions that
the experience, in this way connecting the diverse abstractions that
are called "objects" and "indices", respectively.
are called "objects" and "indices", respectively.
If a suitable framework of object instances can be found to rationalize
If a suitable framework of object instances can be found to rationalize
with respect to its own presumptuous form of analysis and all of
with respect to its own presumptuous form of analysis and all of
the circular viscosities of its "tacit analytic framework" (TAF).
the circular viscosities of its "tacit analytic framework" (TAF).
</pre>
=====1.3.4.10. Sundry Problems=====
1.3.4.10. Sundry Problems
<pre>
There are moments in the development of an analytic discussion when a
There are moments in the development of an analytic discussion when a
thing initially described as a single object under a single sign needs
thing initially described as a single object under a single sign needs
the moment to moment placement of dynamic elements and systematic
the moment to moment placement of dynamic elements and systematic
components with regard to this underlying field of polarities.
components with regard to this underlying field of polarities.
</pre>
=====1.3.4.11. Review and Prospect=====
1.3.4.11. Review and Prospect
<pre>
What has been learned from the foregoing study of icons and indices?
What has been learned from the foregoing study of icons and indices?
The impact of this examination can be sized up in a couple of stages:
The impact of this examination can be sized up in a couple of stages:
it helps to introduce a set of organizing conceptions. Doing this will
it helps to introduce a set of organizing conceptions. Doing this will
be the business of the next four Subsections.
be the business of the next four Subsections.
<pre>
=====1.3.4.12. Objective Plans and Levels=====
1.3.4.12. Objective Plans and Levels
<pre>
In accounting for the special characteristics of icons and indices
In accounting for the special characteristics of icons and indices
that arose in previous discussions, it became necessary to open up
that arose in previous discussions, it became necessary to open up
